In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we show that the worst-case iteration bound for our IPM is $O(6(m+1)^{\frac{3m+4}{2(m+1)}}\Psi _{0}^{\frac{m+2}{2(m+1)}}\frac{1}{\theta }\log \frac{n\mu ^{0}}{\varepsilon })$, where $m>4$.